Formally, given the constraint/observation function \(\mu ({\color {black} x},u)\)  in (REF ) with known \(u\) , a constraint/observation set \(\mathcal {Y}\)  with maximal and minimal values \(\overline{y},\underline{y}\)  (satisfying \(\mu ({\color {black} x},u) \subset \mathcal {Y} \subseteq [\underline{y},\overline{y}]\) ) and a prior (or propagated/predicted) reachable interval \(\mathbb {I}\mathcal {{\color {black} X}}^p=[\underline{{\color {black} x}}^p,\overline{{\color {black} x}}^p]\) , we wish to find an updated/refined interval \(\mathbb {I}\mathcal {{\color {black} X}}^u \subseteq \mathbb {I}\mathcal {{\color {black} X}}^p \) , such that (REF ) holds, i.e., to solve Problem REF . Finding \(\mathbb {I}\mathcal {{\color {black} X}}^u\)  in (REF ) is called the set inversion problem [1]}. To our best knowledge, existing set inversion algorithms/operators either compute subpavings (i.e., unions of intervals) instead of an interval using (conservative) natural inclusions (SIVIA [1]}) or only applies if relatively restrictive monotonicity assumptions hold (\(\mathcal {I}_G\)  [3]}).
